A wavefront sensor is a device for measuring the aberrations of an optical wavefront. Hartmann developed the Hartmann Test over one hundred years ago, yet the Hartmann class of wavefront sensors continues to be the most commonly used type of wavefront sensors to this time.
The first Hartmann Test was simply a screen, a sheet of material with a series of holes cut into it. The Hartmann screen was placed at the opening of a telescope and then viewed with the telescope's optics, either lenses or mirrors. If there was any deviation in the location of the holes of the Hartmann screen observed in the image of the Hartmann screen created by the telescope optics, then a defect was present in the telescope optics. In other words, aberrations were present in the telescope optics.
Shack modified the Hartmann test by adding a lens (also called a lenslet) into each of the holes in the Hartmann screen. The Hartmann screen with lenslets is known as the Shack-Hartmann system. Each lenslet has a controllable focal length, allowing a longer focal length than a hole without a lens could create to be introduced into the system. A hole with no lens will act as a pin-hole camera and cause a spot of light to be formed some distance downstream in the direction of the flow of light.
Liang et al. modified the Shack-Hartmann system by adapting its use to measuring the wavefront of the human eye. See U.S. Pat. No. 6,270,221.
The theory of operation when using a simple Hartmann screen as a wavefront sensor is to pass light through the Hartmann screen, then observe the location shift of the spots formed by the holes. The shift in location of the spot is a direct indicator of the angle of the light that passed through the hole, relative to the perpendicular axis. For example, if light approached and then passed through the Hartmann screen perpendicular to the flat surface of the screen (a flat wavefront), the light would form a spot at a small distance downstream to the flow of light, and the spot would appear to be in the center of the hole when viewed from the downstream side of the Hartmann screen if the observer was looking at the Hartmann screen perpendicularly. However, if the light approached the Hartmann screen at an angle, for example, if the light approached the screen such that the light's source was below the perpendicular axis of the Hartmann screen and rising up, then the points of light formed by the holes would be above the apparent center of the holes of the Hartmann screen. With the use of basic trigonometry, the distance of the lateral shift of the point of light, coupled with the distance that the point of light is away from the hole, can be used to calculate the angle of the approach of light. The spots of light form at various distances downstream from the holes, and this must be either measured or calculated in the conditions at which the light will be analyzed. These distances are known to those skilled in the art of optics.
In the case of measuring light in a manner useful to optical applications, the complex shape of the light wave must be measured. In these cases, each point of light is individually measured for movement, and the angle of light, or in other words, its slope, can be measured at each of the numerous individual locations, allowing a complex analysis to occur.
The angle (or slope) of the approaching light to be analyzed is usually very small in most optical applications. For example, with human eyes, refraction is measured in Diopters. If, for example, an eye had one Diopter of refractive error, the angle of the light to be measured from a 6 mm pupil is only one third of a degree. If light from this eye were passed through a Hartmann screen and formed a spot of light at a distance of 4 mm downstream, the spot will have shifted off-center by only 0.023 mm. Such a small shift can be difficult to detect and measure.
When lenses are added to the Hartmann screen (a Shack-Hartmann wavefront sensor), the distance between the spot of light and the screen can be increased, thereby increasing the lateral movement of the spots for any given angle of light approaching the device. This axial distance could be controlled by the focal distance of the lens. For example, if the same one Diopter light beam described in the preceding paragraph were used with typical Shack-Hartmann lenslet array with lenses having a 20 mm focal distance, the spot would shift 0.115 mm laterally (vs. 0.023 mm along a 4 mm axial distance). This increased lateral movement of 500% results in a 500% improvement to the sensitivity of the system.
However, this increase in sensitivity comes at the price of reducing the range of measurement of the device. By extending the distance that the spots of light formed away from the Hartmann screen, the Shack-Hartmann wavefront sensor causes a simultaneous increase in the variability of the shift in the axial distance that occurs along with the shift in the lateral distance, causing the spots to become no longer in the focus plane of the observing camera, which is used to detect the spot movement. With both systems, the Hartmann Screen and the Shack-Hartmann, as the spots of light shift laterally, they also shift axially, or lengthwise. For example, with a diverging wavefront passing through the system, the spots of light will all appear to be moving radially outward from each other, but they will also be moving further downstream from the holes and/or the lenses. In the case of the Hartmann Screen, the movement in both directions, laterally and axially, is less than the amount of movement caused by the Shack-Hartmann device. The axial movement of the Hartmann Screen spots is considerably less than the axial movement of the Shack-Hartmann spots, and consequently, the spots remain in focus of the observing camera throughout a higher range of measurement than the Shack-Hartmann device.
Hence, the Hartmann Screen has higher dynamic range of measurement but lower sensitivity to small light shifts, while the Shack-Hartmann system has lower dynamic range of measurement but higher sensitivity to small light shifts. Increased sensitivity comes at the expense of range, and increased range comes at the expense of sensitivity in these devices.
Many efforts have been made to overcome this deficiency in the Shack-Hartmann system. A review of the literature in the public domain will yield many examples of such efforts, but all of these efforts require that the system be made more complex with such things as moving optical parts, higher resolution, more expensive cameras, complex sub-pixel analysis, etc.
A different optical system is the Talbot wavefront sensing method (also a concept known for more than one hundred years). Talbot optics are optics made from rulings (a series of parallel lines cut into or etched onto a clear object), or cross gratings, which are two sets of parallel rulings intersecting each other at a cross angle, which cause a self-imaging pattern of lines or cross lines to form in space a predicted distance away from the Talbot optic called “shadow patterns,” with the distance based upon factors such as the wavelength of light and the spacing of the ruling lines. The location of these shadow lines would move based upon the angle of light passing through the Talbot optic, but they too would move only small amounts.
To increase the movement of the shadow patterns, the Moiré effect was employed with the Talbot (or other shadow-creating) optics. U.S. Pat. No. 5,963,300 to Horwitz and U.S. Pat. No. 6,736,510 to Van Heugten describe Talbot wavefront sensing systems with the use of Moiré effects. Horwitz placed a second, identical Talbot optic behind the first Talbot optic, then rotated the second Talbot optic slightly with respect to the first Talbot optic. By doing so, the shadow pattern's movement was amplified, making the movement easier to detect. Both devices described in these patents used rulings or gratings to produce shadows and did not use Hartmann optics with circular apertures to produce light spots of concentrated, focused beams.
A moving shadow pattern (as in Talbot or Talbot Moiré) differs from the moving spots (as in the Hartmann Screen or the Shack-Hartmann device). Hartmann screens do not merely form shadows or shadow patterns, they form focused spots of light due to the holes acting as pinhole cameras, concentrating a beam diameter down to a smaller beam diameter, or a point. Shack-Hartmann devices also do not form shadow patterns; they form focused spots of light due to the lenslets refracting the light, also concentrating a beam diameter down to a smaller beam, or a point. The moving shadow patterns are not as localized and can not be measured for centration as well as the moving spots of Hartmann devices. Other advantages of moving spots versus shadows include that Hartmann-based optics can form spot patterns of light at a narrower plane from polychromatic light, whereas Talbot optics create a thicker plane which cannot be imaged by a camera as easily, if at all. This allows Hartmann-based optics to examine beams of light in multiple wavelengths if necessary, which is particularly useful when measuring the human eye, whereas Talbot based optics are limited to function in narrower wavelength bands of light. Another advantage is that in today's wavefront sensor, CCD cameras are used to view the images. CCD cameras have square pixels aligned in rows and columns, causing aliasing distortions when the shadow lines formed by Talbot optics that utilize rulings or gratings align with the rows of pixels, which interferes with the analysis. Hartmann-based optics create circular spots, which do not create this aliasing problem. Another advantage of Hartmann-based optics is that because the spots formed are circular, more efficient centroiding algorithms may be used, which cannot be used as efficiently upon the lines or squares formed by Talbot optics.
There is a need for wavefront sensors that can achieve both high sensitivity and a high dynamic range of measurement. There is also a need for wavefront sensors that result in a high image quality. There is also a need for wavefront sensors that are small, lightweight, inexpensive, versatile, and simple.